We propose the use of a mean-quadratic-variation criteria to determine an optimal trading strategy 5 in the presence of price impact. We derive the Hamilton Jacobi Bellman (HJB) Partial Differential 6 Equation (PDE) for the optimal strategy, assuming the underlying asset follows Geometric Brownian
A continuous time mean variance (MV) problem optimizes the biobjective criteria (V, E), representing variance V and expected value E, respectively, of a random variable at the end of a time horizon T. This problem is computationally challenging since the dynamic programming principle cannot be directly applied to the variance criterion. An embedding technique has been proposed in [D.
We consider the energy Laplacian ν on the Sierpinski gasket (SG), which is defined by the standard self-similar energy E and the Kusuoka measure, and is different from the standard self-similar Laplacian . We study the local behavior of function u ∈ dom k ν near a boundary point q 0 . We define jets of local derivatives at q 0 and estimate the decay rate of u near q 0 in terms of the vanishing of jet. This can be used to define Taylor approximating polynomials with error estimates. Analogous results are known for the standard Laplacian, but the results here are quite different. We also confirm experimentally the absolute continuity of different energy measures, and give experimental evidence that the density is p-integrable for p < log(15) log(9) .
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